Former deputy prime minister Wayne Swan has switched his position on same-sex marriage, conceding he was "wrong" to oppose it, as new figures put Federal Parliament less than a handful of votes away from backing the landmark reform.

Australian Marriage Equality figures show that Parliament is on the brink of having enough support to legislate same-sex marriage, needing just four more votes to pass a bill in the House of Representatives. In the Senate, it is calculated a bill could pass with a majority of one.

In a sign of the growing momentum in Canberra, Mr Swan has announced he now supports same-sex marriage. The member for Lilley in Brisbane opposed same-sex marriage during the Labor years in government, voting against the reform when it came before Parliament in 2012.

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Mr Swan told Fairfax Media he had found it "increasingly difficult" to reconcile his views about same-sex marriage with his support for economic and social equality.

Wayne Swan Credit:Alex Ellinghausen

"I've come to the conclusion that, basically, I was wrong," he said.

In the wake of a raft of Labor MPs recently declaring their support for same-sex marriage, including Chris Bowen, Ed Husic and Bernie Ripoll, AME has done a fresh calculation of support for the reform in Federal Parliament. It also says 13 unnamed Coalition MPs have switched their position to supporting same-sex marriage since the start of the year.

AME is confident there are now at least 72 lower house MPs who would vote for same-sex marriage, which is just four votes shy of the 76 required to pass a bill.

In the Senate, AME estimates same-sex marriage has 39 supporters and so would pass with a majority of one.

This is based on the assumption that Liberal MPs were allowed a free vote and includes MPs who have privately indicated they back same-sex marriage.

Australian Marriage Equality national director Rodney Croome said the small number of Coalition members publicly in favour of same-sex marriage was the "tip of an iceberg of support".

"Given a cross-party free vote, the reform has a good chance of passing," Mr Croome said.

Some Liberal MPs have been hesitant to speak out in support of same-sex marriage because the party does not have a free vote, and due to sensitivity about preselections for the next federal election.

In the lower house, AME says there are 20 supporters - from different parties - who have not declared their position publicly. In the Senate, it has identified eight private supporters, also from different parties.

Mr Croome said a lot of credit for the shift in numbers goes to "everyday Australians" who have lobbied their local MPs with personal stories.

Previous estimates from advocates and same-sex marriage backers in Canberra have played down the likelihood of the reform passing before the next election. One recent estimate had same-sex marriage as much as 20 votes away from a majority in the lower house.

There continues to be a question mark over the Liberal Party's exact position on same-sex marriage. While the party and Prime Minister Tony Abbott do not support same-sex marriage, Mr Abbott has said that the issue of a free vote would be a matter for the post-election party room.

Liberal MPs have so far passed up opportunities to discuss it in party room meetings - despite Libertarian senator David Leyonhjelm​ introducing a "freedom to marry" bill in the Senate last year.